Nexus 7 bookmarks - help please

Is there a straightforward way to manage bookmarks across different browsers and devices? I use IE at work (not my choice); Firefox at home and my Nexus 7 comes with Chrome as the default.

When I first set up my Nexus it managed to import some bookmarks from Firefox. I think this was because I had signed into my Google account and the Nexus had copied them from my Google account. Possibly. (Does that sound plausible?). Anyway, these bookmarks now sit in a folder called ‘Imported from Firefox’ on the Nexus.

My ‘problem’ is I realise my home-based Firefox bookmarks are well out of date with the ones I use at work. I also haven’t been able to work out how to update or refresh the bookmarks from Firefox on the Nexus. I tried signing into my Google account last night on the home PC and changing a few bookmarks in Firefox, then syncing the Nexus, but there was no change to the Bookmarks on the Nexus.

So I'd like to sync my bookmarks across different devices if possible. My thoughts so far are to:
1. Export my work IE bookmarks as a file
2. Install Chrome on the home PC
3. Import my work bookmarks to home PC and Chrome
4. Sync Chrome between the Nexus and the home PC (I can work out how to do this bit).
5. Regularly export work bookmarks to home to keep them updated.

Is there a simpler way, or a way that avoids me having to install Chrome at home?
Thanks

If you can somehow sync your work IE with IE on your home computer when you install chrome on your home PC you can import the bookmarks. Then login to chrome with your gmail account that you use on your Nexus and it will sync across.

Thats the only way I can think of. I just use chrome everywhere (PC/phone/nexus) and it plays very nicely.